Question

Ron attends a party. He wants to limit his food intake to 22g ?protein, 25g ?fat, and 37g carbohydrate. According to the health conscious? hostess, the marinated mushroom caps have 1g? protein, 2g? fat, and 3g? carbohydrate; the spicy meatballs have 4g? protein, 3g? fat, and 7g? carbohydrate; and the deviled eggs have 3g? protein, 4g? fat, and 2g carbohydrate. How many of each snack can he eat to obtain his? goal? mushrooms___meatboals____eggs____

Answer 1

There are a lot of ? marks which we are ignoring. Also, we presume that the nutrient contents of the food items described are per helping.

Let Ron take x,y and z helpings of marinated mushroom caps, spicy meatballs and deviled eggs respectively. Then, we have x+4y+3z = 22…(1), 2x+3y+4z = 25…(2) and 3x+7y+2z = 37…(3).

The augmented matrix of this linear system is A =

1	4	3	22
2	3	4	25
3	7	2	37

To solve the3 above linear system, we have to reduce A to its RREF which is

1	0	0	4
0	1	0	3
0	0	1	2

Hence, x = 4,y = 3 and z = 2.

Thus, Ron should eat 4,3 and 2 helpings of marinated mushroom caps, spicy meatballs and deviled eggs respectively to achieve his goal.